Theorems · Theorem · commutative algebra
smoothingSeminorm_apply_of_map_mul_eq_mul
∀ {R : Type u_1} [inst : CommRing R] (μ : RingSeminorm R) (hμ1 : μ 1 ≤ 1) (hna : IsNonarchimedean ⇑μ) {x : R},
(∀ (y : R), μ (x * y) = μ x * μ y) → (smoothingSeminorm μ hμ1 hna) x = μ xIf μ 1 ≤ 1, μ is nonarchimedean, and ∀ y : R, μ (x * y) = μ x * μ y, then
smoothingSeminorm μ x = μ x.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 212 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement · cited by 25,697
- CommRingstatement and proof · cited by 17,173
- IsNonarchimedeanstatement and proof · cited by 77
- RingSeminormstatement and proof · cited by 58
- smoothingSeminormstatement · cited by 5
- smoothingFun_apply_of_map_mul_eq_mulproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- exists_nonarchimedean_pow_mul_seminorm_of_finiteDimensionalproof · cited by 5